Time remaining:
Hypothesis test with an alpha level

Statistics
Tutor: None Selected Time limit: 1 Day

You work for a bottling company. They claim that 16 ounces of beverage goes into every bottle. You have taken a random sample of 100 bottles. You found that the sample mean was 16.1 with a sample standard deviation of 0.4 ounces. You want to determine if the number of ounces in the bottle is different than 16. Perform the appropriate hypothesis test at an alpha level of 0.05

Mar 24th, 2015

Since we don't know the population standard deviation (only the sample SD) we should use the t-distribution here. Our degrees of freedom will be the sample size, n=100.

First, find the standard error of the sample mean. This will be:

SEM = sample sd / sqrt(n), where n is the sample size.

SEM = 0.4 / sqrt(100) = 0.04.

Next, find the t value associated with our measurement of 16.1. This will be:

(measurement - pop mean) / SEM

t = (16.1-16)/0.04

= 2.5

Now we can go in two different ways (they'll give you the same answer) to test the hypothesis. One, find the probability of seeing a lower t-value than 2.5 for our degrees of freedom:

P(t<2.5, df = 100) = 0.993

Since this is greater than (1 - alpha/2), we reject the null hypothesis. We'd do the same if it was less than alpha/2, i.e. the null hypothesis would be accepted for alpha/2 < P(t) < 1-alpha/2.


Alternatively, you can find the critical t for a 95% confidence interval (100% - alpha) using the inverse. Remember it's two-tailed, so the probability you use is (1-alpha/2), not (1-alpha) since you need the 95% range in the middle so it stretches from 2.5% to 97.5%:

(t | P=0.975, df = 100) = t.inv(0.975,100) = 1.984


Since the magnitude of the t-stat we found (2.5) is greater than the critical t for the test (1.984), we reject the null hypothesis (note that if we found -2.5, we'd also reject since the magnitude of -2.5 is 2.5).


Mar 24th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Mar 24th, 2015
...
Mar 24th, 2015
Dec 8th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer